Due to their versatile properties, robust behavior, facile processability and low cost, organic polymers have become the material of choice for an increasing number of mature and cutting-edge technologies. In the last decade or so, a new class of polymers capable of responding to external electrical stimulation by displaying significant size or shape change has emerged. These responsive materials, collectively referred to as electroactive polymers (EAPs), are broadly classified as electronic or ionic according to their operational mechanism. Electronic EAPs generally exhibit superior performance relative to ionic EAPs in terms of actuation strain, reliability, durability and response time. Among electronic EAPs, dielectric elastomers exhibit the most promising properties that mimic natural muscle for use in advanced robotics and smart prosthetics, as well as in haptic and microfluidic devices. Elastomers derived from homopolymers such as acrylics and silicones have received considerable attention as dielectric EAPs, whereas novel dielectric EAPs based on selectively swollen nanostructured block copolymers with composition-tailorable properties have only recently been reported. Here, we provide an overview of various EAPs in terms of their operational mechanisms, uses and shortcomings, as well as a detailed account of dielectric elastomers as next-generation actuators.